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25 Remote Warehouse Mathematics- Algebraic Geometry

Lectures on vector bundles

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Lectures on vector bundles Cover

 

Synopses & Reviews

Publisher Comments:

This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Synopsis:

This work consists of two courses on the moduli spaces of vector bundles. The first is introductory, and assumes very little background; the second is more advanced and takes the reader into current areas of research. This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Synopsis:

This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Description:

Includes bibliographical references (p. 245-248) and index.

Table of Contents

Part I. Vector Bundles On Algebraic Curves: 1. Generalities; 2. The Riemann-Roch formula; 3. Topological; 4. The Hilbert scheme; 5. Semi-stability; 6. Invariant geometry; 7. The construction of M(r,d); 8. Study of M(r,d); Part II. Moduli Spaces Of Semi-Stable Sheaves On The Projective Plane; 9. Introduction; 10. Operations on semi-stable sheaves; 11. Restriction to curves; 12. Bogomolov's theorem; 13. Bounded families; 14. The construction of the moduli space; 15. Differential study of the Shatz stratification; 16. The conditions for existence; 17. The irreducibility; 18. The Picard group; Bibliography.

Product Details

ISBN:
9780521481823
Editor:
Bollobas, B.
Publisher:
Cambridge University Press
Editor:
Bollobas, B.
Editor:
Bollobas, Bela
Author:
Bollobas, B.
Author:
J, Le Potier
Author:
J. Le Potier
Author:
Fulton, W.
Author:
Le Potier, J.
Author:
Sarnak, P.
Author:
Kirwan, F.
Author:
Le Potier, Joseph
Author:
Katok, A.
Author:
Macioca, Antony
Location:
Cambridge ;
Subject:
Applied
Subject:
Geometry - General
Subject:
Geometry - Algebraic
Subject:
Vector bundles.
Subject:
Topology - General
Subject:
Mathematics-Algebraic Geometry
Series:
Cambridge Texts in Applied Mathematics
Series Volume:
O54
Publication Date:
19970131
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
1 line diagram
Pages:
260
Dimensions:
5.98x9.01x.74 in. 1.22 lbs.

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Related Subjects

History and Social Science » Law » General
Religion » Comparative Religion » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Topology

Lectures on vector bundles New Hardcover
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Product details 260 pages Cambridge University Press,1997. - English 9780521481823 Reviews:
"Synopsis" by , This work consists of two courses on the moduli spaces of vector bundles. The first is introductory, and assumes very little background; the second is more advanced and takes the reader into current areas of research. This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.
"Synopsis" by , This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.
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